Upgrading Worth it on my Machine

My specs are out of date. I have a 6600k @ 3.6GHZ , 16 GB Gskill DDR4 Ram, Power supply is the same, this is my motherboard GPU-/MB - MB - GIGABYTE GA-P55-USB3

My current Video Card is an ASUS STRIX GeForce GTX 960 Overclocked 4 GB DDR5 128-bit . I started playing Rainbow Six siege on the PC and it looks like a super nintendo game. Is there a card you could recommend so I could vastly improve my experience. I was looking at the GTX 1080 which was supposed to be 580 but because of mining is almost double the price.

Well, the 1080 is way faster than a RX 580. A GTX 1060 6GB is about the equivalent of a RX 580, so maybe consider get that. I really wouldn't get anything more than a GTX 1070 for Siege. The CPU like @beers said is fine.